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Similar to Dijkstra_Algorithm with illustarted example
Dijkstra_Algorithm with illustarted example
- 1. 1 Dijkstra’s Algorithm Data Structures& Algorithms
- 2. 2 Single-Source Shortest-Paths Problem Problem: given a connected graph G with non-negative weights on the edges and a source vertex s in G, determine the shortest paths from s to all other vertices in G. Useful in many applications (e.g., road map applications) 14 10 3 6 4 5 2 9 15 8
- 3. 3 Single-Source Shortest-Paths Forinstance, the following edges form the shortest paths from node A H B C G E D F A 14 10 3 6 4 5 2 9 15 8
- 4. 4 Single-Source Shortest-Paths H BC G E D F A 14 10 3 6 4 5 2 9 15 8 • Hint: does this problem looks similar? • Can we modify Prim’s algorithm to solve this problem?
- 5. 5 Dijkstra’s Algorithm Solvesthe single-source shortest paths problem Involves keeping a table of current shortest path lengths from source vertex (initialize to infinity for all vertices except s, which has length 0) Repeatedly select the vertex u with shortest path length, and update other lengths by considering the path that passes through that vertex Stop when all vertices have been selected Could use a priority queue to facilitate selection of shortest lengths » Here, priority is defined differently from that of the Prim’s algorithm » Like Prim’s algorithm, it needs to refine data structure so that the update of key-values in priority queue is allowed » Like Prim’s algorithm, time complexity is O( (n + m) log n )
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